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Theoretical analysis demonstrates subeulerian embeddability in orientations of cubic graphs of order at least 14, establishing universal Eulerian extension bounds.
A graph is subeulerian if it is a spanning subgraph of an eulerian graph. A digraph D is eulerian if and only if D is connected and d+(x)=d-(x) for every vertex x∈V(D). An orientation G⃗ of a graph G is a digraph obtained from G by replacing each edge xy of G with an arc xy or yx. An oriented graph is an orientation of a simple graph. An oriented graph is said to be subeulerian if it is a spanning subdigraph of an Eulerian oriented graph. In this paper, we show that any orientation G⃗ of a cubic graph G of order n≥14 is subeulerian.
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